Thursday, 8 March 2007

Gettierising Nozick

Over at The Web of Belief, I lay out a Gettier case against local reliabilism (which is itself based on an earlier post of mine, Undescriminating Reliabilism). Let's call my proposed Gettier case against local reliabilism GLR. The version of local reliability I took as my target was admittedly quite simple, so here I will attempt to apply GLR to a much more sophisticated version of local reliability—namely, Nozick’s counterfactual account. Nozick [1981, p. 179] argues that the true belief that p is knowledge only if:

(N1) If p were true, then S would believe that p(N2) If p were not true, then S would not believe that p1

Following David Lewis [1973] we may say that (N1) and (N2) are true, as counterfactual statements, iff in possible worlds near to the actual world, if p is true, S believes that p, and if p is false S does not believe that p. Nozick recommends that we assess (N1) and (N2) by reference to what is the case in all nearby possible worlds. Roughly, a world may be described as ‘nearby’ if it is only slightly different from the actual world and ‘distant’ if it is radically different.

The following reply to GLR seems available to Nozick. Let us suppose that the set of nearby possible worlds include ones in which the computer is running a different program or is missing altogether. In such nearby worlds, although there is a red cube in the box, there is no hologram of a red cube. Since in such a world the subject would not believe that (a) although (a) is true, (N1) has not been satisfied.

One initial difficulty with this reply is that it is not immediately clear that worlds in which the computer is running a different program or is missing altogether should be considered nearby. But let us, for the sake of argument, assume that such worlds are in fact nearby.

Even so, Nozick’s strategy for responding to GLR proves too much, since it also impugns cases in which the subject intuitively has knowledge.

The ‘Jesse James’ Counterexample: Consider the case of the Jesse James Bank Robbery, as described by Craig [1990]:

Jesse James, the reader will recall, is riding away from the scene of the crime with his scarf tied round his face just below the eyes in the approved manner. The mask slips, and a bystander, who has studied the ‘wanted’ posters, recognises him. The bystander now knows, surely, that it was James who robbed the bank. But Nozick has a problem: there is a possible world, and a ‘close’ one, in which James’ mask didn’t slip, or didn’t slip until he was already past the bystander; and in that world the bystander wouldn’t believe that James robbed the bank, although it would still be true that he did. So Nozick’s condition [N1] is not satisfied, and he is threatened with having to say that the bystander doesn’t know that it was James, even though the mask did slip. So his analysis looks like ruling out something which is as good a case of knowledge as one could wish for [p. 22].

Nozick is already equipped with a reply to the ‘Jesse James’ counterexample, akin to that employed in the Grandma case [See endnote 1]. In brief, he may simply argue that in worlds in which the mask did not slip, the method employed by the bystander would be different. Thus, given the version of Nozick’s counterfactuals revised to include the subject’s method, worlds in which the mask did not slip would not be included in the relevant nearby possible worlds.

However, to the extant that this reply is effective in preserving the bystanders knowledge in the Jesse James case, it is also effective at preserving the GLR subject’s ‘knowledge’ that (a). In GLR, the computer program, as the locus of reliability, constitutes part of the method by which S arrives at her belief that (a). Thus, by (N1*), all worlds in which the computer program is different or the computer is missing, a different method is being used and that world eo ipso fails to count as nearby.

Endnote:

1Counter examples such as the Grandma case has prompted Nozick [1981, p. 179] to revise (N1) and (N2), limiting them to the same method (i.e., vision):

(N1*) If p were true, S (using M) would believe that p

(N2*) If p were not true, then S (using M) would not believe that p

References:

Craig, E. [1990], Knowledge and the State of Nature. Oxford: Clarendon Press.

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The Reasoner

Today my self-esteem hit an all time low when I stumbled across an argument proving conclusively that I don't exist. I’m quite distressed. This probably explains why my jeans are so loose-fitting. What’s equally upsetting is that I learned that non-existence does not exempt one from local or federal taxes.